An Improved Alternating Direction Method of Multipliers for Matrix Completion

[1] Argyriou A, Evgeniou T, Pontil M, Multi-task feature learning, Advances in Neural Information Processing Systems, 19, 2007, 41-48. Search in Google Scholar

[2] Cai J F, Candès E J, Shen Z, A singular value thresholding algorithm for matrix completion, SIAM Journal on Optimization, 20, 4, 2010, 1956-1982. Search in Google Scholar

[3] Candès E J, Tao T, The power of convex relaxation: near-optimal matrix completion, IEEE Transactions on Information Theory, 56, 5, 2010, 2053-2080. Search in Google Scholar

[4] Chen C, Chan R H, Ma S, et al, Inertial proximal ADMM for linearly constrained separable convex optimization, SIAM Journal on Imaging Sciences, 8, 4, 2015, 2239-2267. Search in Google Scholar

[5] Chen C, He B, Yuan X, Matrix completion via an alternating direction method, IMA Journal of Numerical Analysis, 32, 1, 2012, 227-245. Search in Google Scholar

[6] Eckstein J, Some saddle-function splitting methods for convex programming, Optimization Methods and Software, 4, 1, 1994, 75-83. Search in Google Scholar

[7] Fazel M, Matrix rank minimization with applications, PhD Thesis, Stanford University, 2002. Search in Google Scholar

[8] Fazel M, Hindi H, Boyd S P, Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices, Proceedings of the 2003 American Control Conference, 2003. Search in Google Scholar

[9] Fazel M, Pong T K, Sun D, et al, Hankel matrix rank minimization with applications to system identification and realization, SIAM Journal on Matrix Analysis and Applications, 34, 3, 2013, 946-977. Search in Google Scholar

[10] Gabay D, Mercier B, A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Computers & Mathematics with Applications, 2, 1, 1976, 17-40. Search in Google Scholar

[11] Glowinski R, Numerical methods for nonlinear variational problems, New York: Springer, 1984. Search in Google Scholar

[12] Glowinski R, Le Tallec P, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, Society for Industrial and Applied Mathematics, 1989. Search in Google Scholar

[13] Hale E T, Yin W, Zhang Y, Fixed-point continuation for l₁-minimization: methodology and convergence, SIAM Journal on Optimization, 19, 3, 2008, 1107-1130. Search in Google Scholar

[14] He B, Ma F, Yuan X, Optimally linearizing the alternating direction method of multipliers for convex programming, Computational Optimization and Applications, 75, 2020, 361-388. Search in Google Scholar

[15] Lin Z, Chen M, Ma Y, The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices, ArXiv:1009.5055, 2010. Search in Google Scholar

[16] Ma S, Goldfarb D, Chen L, Fixed point and Bregman iterative methods for matrix rank minimization, Mathematical Programming, 128, 2011, 321-353. Search in Google Scholar

[17] Malitsky Y, Golden ratio algorithms for variational inequalities, Mathematical Programming, 184, 2020, 383-410. Search in Google Scholar

[18] Ouyang Y, Chen Y, Lan G, et al, An accelerated linearized alternating direction method of multipliers, SIAM Journal on Imaging Sciences, 8, 1, 2015, 644-681. Search in Google Scholar

[19] Shefi R, Teboulle M, Rate of convergence analysis of decomposition methods based on the proximal method of multipliers for convex minimization, SIAM Journal on Optimization, 24, 1, 2014, 269–297. Search in Google Scholar

[20] Spyromitros-Xioufis E, Tsoumakas G, Groves W, et al, Multi-target regression via input space expansion: treating targets as inputs, Machine Learning, 104, 2016, 55-98. Search in Google Scholar

[21] Toh K C, Yun S, An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems, Pacific Journal of Optimization, 6, 3, 2010, 615-640. Search in Google Scholar

[22] Tomasi C, Kanade T, Shape and motion from image streams: a factorization method, International Journal of Computer Vision, 9, 2, 1992, 137-154. Search in Google Scholar

[23] Wang X, Yuan X, The linearized alternating direction method of multipliers for Dantzig selector, SIAM Journal on Scientific Computing, 34, 5, 2012, A2792-A2811. Search in Google Scholar

[24] Xue H Y, Zhang S, Cai D, Depth image inpainting: improving low rank matrix completion with low gradient regularization, IEEE Transactions on Image Processing, 26, 9, 2017, 4311-4320. Search in Google Scholar